# Show that the propositions p and p v (p ^ q) are logically equivalent? Must do a truth table.

Jul 16, 2018

See below

#### Explanation:

This definitely looks like homework, so I don't intend to do the work for you, since I am in doubt how much you actually will learn from someone else doing the work for you.

But a suggestion: Create a Venn diagram and a truth table based on that.

Jul 19, 2018

#### Explanation:

$\text{The Exp.} = p \vee \left(p \wedge q\right)$,

=(pvvp)^^(pvvq)...[because," distributive law]",

=p^^(pvvq)...[because," idempotent law]".

But, $p \Rightarrow p \wedge q$.

$\therefore \text{The Exp.} = p$, as desired!